I just entered the BS works about 9 months ago after being a TS guy for over
a decade. Yes, it does curves and resawing as expected, but the surprise
benefit is stopped interior/stopped cuts and the ability to safely and
quickly freehand quick & dirty (or precise for that matter) things:

Example: I want to hold a long piece with pointy ends between the dogs on my
bench. Any significant pressure directly on the pointy ends would damage
them. Solution: take two little pices of scrap wood flat against each dog,
set the piece on top of them and trace the ends onto the little squares. Cut
out trace lines on the BS. Voila, custom cauls. That took about 90 seconds.

My general impression is that *most* of what I want to do with a bandsaw
can be done with the combination of a jig saw and table saw. (hey I can
resaw up to 6" with my TS). But w/ a BS many of these operations are just
easier and safer. It is a really nice tool to have around. I think that
would will go to that saw for more than just curves and resawing. Things for
which you might have previously used another tool.

I'm really glad I have one now.

-Steve